Which of the following numbers is a factor of 160? ${7,9,10,11,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $160$ by each of our answer choices. $160 \div 7 = 22\text{ R }6$ $160 \div 9 = 17\text{ R }7$ $160 \div 10 = 16$ $160 \div 11 = 14\text{ R }6$ $160 \div 14 = 11\text{ R }6$ The only answer choice that divides into $160$ with no remainder is $10$ $ 16$ $10$ $160$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $160$ $160 = 2\times2\times2\times2\times2\times5 10 = 2\times5$ Therefore the only factor of $160$ out of our choices is $10$. We can say that $160$ is divisible by $10$.